Mathematical Physics, Geometric Analysis, Nonlinear Partial Differential Equations.Recent teaching experiences:
(1)Practical track of ordinary differential equations in Caltech, fall 2015, large class of 198 students;
(2)Ordinary differential equations in Caltech, fall 2016, large class of 237 students;
(3) Ordinary differential equations in Binghamton University, fall 2017, Spring 2018, Fall 2018, classes of about 30 students,
(4) topics in geometric flows, Spring 2018; dynamical systems, Fall 2018; complex analysis, spring 2019.Published or Submitted Papers
(1) Zhou Gang, Perturbation expansion and N-order Fermi Golden rule, Journal of Mathematical Physics, 48(5):053509, 23, 2007.
(2) Zhou Gang and I.M.Sigal Soliton dynamics of nonlinear Schroedinger equations, Geometric and Functional Analysis, 116(6):1377--1390, 2006.
(3) Zhou Gang and I.M.Sigal, Asymptotic Stability of Nonlinear Schroedinger Equations with Potential, Reviews in Mathematical Physics, 17(10):1143--1207, 2005.
(4) S. Dejak, Zhou Gang, I.M.Sigal and S. Wang, Blow-up Problem of Nonlinear Heat Equations, Advances in Applied Mathematics, 40 (2008), no. 4, 433--481.
(5) Zhou Gang and I.M.Sigal, Relaxation To Trapped Solitons in Nonlinear Schroedinger Equations with Potential, Advances in Mathematics, 216(2):443--490, 2007.
(6) Zhou Gang and I.M.Sigal, Neck Pinching Dynamics Under Mean Curvature Flow, Journal of Geometric Analysis, 19 (2009), no. 1, 36--80
(7) Zhou Gang and Michael Weinstein, Dynamics of Nonlinear Schroedinger/Gross-Pitaevskii Equations; Mass Transfer in Systems with Solitons and Degenerate Neutral Modes, Analysis and PDE, 1 (2008), no. 3, 267--322.
(8) Zhou Gang and Michael Weinstein: Equipartition of Energy of nonlinear Schroedinger equations, Applied Mathematics Research Express, AMRX 2011, no. 2, 123-181.
(9) Juerg Froehlich, Zhou Gang and Avy Soffer: Some Hamiltonian Models of Friction, Journal of Mathematical Physics, 52, 083508 (2011). Selected for September 2011 issue of Virtual Journal of Atomic Quantum Fluids.
(10) Juerg Froehlich and Zhou Gang: Exponential Convergence to the Maxwell Distribution For Some Class of Boltzmann Equations, Communications in Mathematical Physics, Volume 314, Issue 2, pp 525-554.
(11) D.Knopf, Zhou Gang and I.M.Sigal: Neckpinching Dynamics of Asymmetric Surface Evolving by Mean Curvature Flow, to appear in Memoirs of the American Mathematical Society & arXiv:1109.0939v1
(12) Daniel Egli and Zhou Gang: Some Hamiltonian Models of Friction II, Journal of Mathematical Physics, 53, 103707 (2012)
(13) Juerg Froehlich, Zhou Gang and Avy Soffer: Friction in a Model of Hamiltonian Dynamics, Communcations in Mathematical Physics, Volume 315, Issue 2, pp 401-444
(14) Juerg Froehlich and Zhou Gang: On the theory of slowing down gracefully, Pramana, Journal of Physics, Vol. 78, No. 6, June 2012, pp 865-874
(15) Daniel Egli, Juerg Froehlich, Zhou Gang, Arick Shao and Israel Michael Sigal: Hamiltonian dynamics of a particle interacting with a wave field, Communication in Partial Differential Equations, Volume 38, Issue 12, 2013, Page 2155-2198
(16) Juerg Froehlich and Zhou Gang: Ballistic Motion of a Tracer Particle Coupled to a Bose gas, Advances in Mathematics, 259C (2014), pp. 252-268
(17) D.Knopf and Zhou Gang: Universality in mean curvature flow neckpinches, Duke Math. J. 164 (2015), no. 12, 2341-2406.
(18) Juerg Froehlich and Zhou Gang: Emission of Cherenkov Radiation as a Mechanism for Hamiltonian Friction, Advances in Mathematics, 264, Oct 2014.
(19) Zhou Gang: A Resonance Problem in Relaxation of Ground States of Nonlinear Schroedinger Equations, arXiv:1505.01107.
(20) Rupert Frank and Zhou Gang: Derivation of an effective evolution equation for a strongly coupled polaron, Anal. PDE 10 (2017), no. 2, 379–422. .
(21) Thomas Farrell, Zhou Gang, Dan Knopf, Pedro Ontaneda: Sphere Bundles with 1/4-pinched Fiberwise Metrics, Trans. Amer. Math. Soc. 369 (2017), no. 9, 6613–6630..
(22) Zhou Gang, Philip Grech: An Adiabatic Theorem for the Gross-Pitaevskii Equation, Comm. Partial Differential Equations 42 (2017), no. 5, 731–756..
(23) Zhou Gang: Exponential Convergence to the Maxwell Distribution For Spatially Inhomogenous Boltzmann Equations, to appear in Reviews in Mathematical Physics, arXiv:1603.06642.
(24) Zhou Gang: On the dynamics of formation of generic singularities of mean curvature flow, to appear in Duke Mathematical Journal, arXiv:1708.03484.
(25) Zhou Gang: A decription of a space-and-time neighborhood of generic singularities formed by mean curvature flow, arXiv: 1803:10903.
(26) Zhou Gang and Shengwen Wang: Precise asymptotics near a pinched disk singularity formed by mean curvature flow, arxiv:1904:04300.
(27) Rupert Frank and Zhou Gang: A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations, arXiv:1906.07908